The surfaces of wafers are polished to prepare them for the various processes during which devices are formed in the surface of the wafer. Polishing provides a smooth surface and removes irregularities that interfere with the various diffusion and masking processes utilized in making uniform devices across the surface of the wafer. Polishing is accomplished by mounting several semiconductor wafers in openings in a wafer holder and putting the wafers and holder between two polishing plates that have polishing pads thereon. The wafer holder is rotated and rolled around the periphery of the polishing machine to provide a planetary motion of the wafers during polishing. The movement of the wafer against the polishing pad is used in conjunction with an abrasive slurry of a fine particle size to provide the desired smoothness. One problem encountered with this process is that, although various controllable factors affecting polishing may be controlled, nonflat polishing occurs. Particularly, non-flatness occurs at the edge of the wafer, with the wafer edge receiving more polishing than the central portions, resulting in a "pillow-shaped" wafer. This provides an undesired tapering of the wafer from the center to the edges.